This technical report drawn up by Eng. Fabio Menardo aims to deepen the functioning of AMDesign, plug-in of the commercial software SAP2000 ®, developed by ISAAC Anti-seismic in collaboration with CSI Italy, to allow the structural designer to insert active control systems for seismic protection within the numerical calculation models for applications in civil engineering.
What does AMDesign allow to do?
AMDesign allows you to design real active inertial dampers (in English Active Mass Damper) to study the dynamic behavior of structures subject to seismic action.
Furthermore, the software allows to investigate the mechanical characteristics of the system to verify its correct functioning, just as if it were installed on a real structure. In this way, not only is it possible to evaluate the improvement made by the active system on the building, but it is also possible to keep track of the performance of the AMDs in order to optimize the control parameters.
AMDesign guarantees excellent reliability in terms of dynamic simulations in step whether linear or non-linear, allowing a good flexibility in the definition of the parameters involved while providing a simple and intuitive calculation environment.
It is necessary to create a numerical model of the structure within the latter in order to subsequently be able to design the active control system through the plug-in AMDesign.
In the input structural model it is important that the most important characteristics of the structure are defined, in such a way as to carry out the design of the AMDs within a simulation that reflects the real dynamic behavior of the building in question. Therefore, it will be necessary to create an .sdb file that contains the geometry of the structure, the materials used, the sections of the members, the appropriate constraints, the acting loads, the masses involved and other aspects, some of which will be explored further on in the item.
Once the template has been created, you can start the AMDesign application and load the .sdb file.
In this phase the application will automatically start an instance of SAP2000 ® which will allow the user to interact with the structural calculation software while using AMDesign so as to allow complete interoperability between the two programs.
The panels present within the plug-in, which will be investigated in more detail in the rest of the article, are listed and briefly described below:
- modal analysis to be able to carry out an eigenvalue analysis;
- active control design to be able to design the active control system;
- showarchitecture to view the newly designed system within the model;
- time history analysis setup to set the properties of the analyzes to be performed;
- run analysis to be able to carry out the analyzes set;
- results structure to view the results obtained on the structure side;
- results control to view the results obtained on the control system side;
- save model and export data to be able to save the load cases created and allow the analysis to be carried out directly from the SAP2000 software.
How to design an active control system through AMDesign?
Eigenvalue analysis
The AMDesign application allows you to perform, as a first operation and after selecting a mass source previously defined in SAP2000 ®, an eigenvalue analysis to study the linear dynamic behavior of the analyzed structure.
This aspect is important because it allows to define, in the first instance, the dynamic characteristics of the construction, highlighting any fragility to be protected during the design phase of the system.
The software provides the results both in tabular form, where the periods and frequencies of the first vibrating modes of the structure are shown, and in graphic form through a panel that gives the possibility to view the modal forms.
You can scale the charts by inserting one ScaleFactor.
Active control system design
This panel constitutes the heart of the application, as it allows to design the active control system for the seismic protection of the analyzed structure.
In this tab it is possible, first of all, to define the type of Active Mass Damper to be used within the numerical simulations. The program allows you to choose between two preset solutions, relating to the systems that Isaac Antisismica offers on the market. Through command Advanced Options it is possible to investigate the characteristics of the selected system, which include the plate data of the system itself. This information is briefly listed below:
- nominal data of the system;
- system peak data;
- data relating to the measurement system that will be installed, such as the noise of the sensors (parameter extractable from the manufacturer's data sheet), and the use of any filters;
- transfer function to allow to define the real dynamics of the system;
- other parameters related to the control, such as for example the parameter relating to the activation threshold which identifies the acceleration limit level of the ground at the base of the structure, such that the machines installed on the roofing surface come into operation.
These parameters are partially editable. In fact, the modification of some parameters that are specific to the chosen system is not allowed.
In any case, AMDesign, to ensure maximum flexibility in the introduction of systems, allows you to define Active Mass Damper ad hoc by selecting the option from the drop-down menu Future release, thus allowing you to freely modify the input parameters of the systems, if you want to insert customized systems.
A Sky-Hook control algorithm is implemented inside the application to simulate the behavior of AMDs. The control force of each i-th machine is defined as:
𝐹𝑐, 𝑖= −𝐺𝑆𝐻, 𝑖∙ ((𝑣𝑡, 𝑖−𝑣𝑏, 𝑖) = - 𝐺𝑆𝐻, 𝑖∙ 𝑣𝑟𝑒𝑙, 𝑖
Where:
- 𝑣𝑡, 𝑖 is the speed of the measuring point positioned in correspondence with the i-th machine, on the covering plane, along the direction of application of the force;
- 𝑣𝑏, 𝑖 is the speed of the ground floor of the building at a point vertically aligned with the i-th machine, always in the direction of application of the force of the machine itself;
- 𝐺𝑆𝐻, 𝑖 is the gain (also called Gain) set on the i-th machine. The gain 𝐺𝑆𝐻, 𝑖 defines the constant of direct proportionality between the relative speed of the roof and the applied control force. The negative sign guarantees that the machine generates a force that “counteracts” the action of the earthquake and that it always has a dissipative behavior: in fact, the machine ideally acts as a viscous element placed between the base and the top of the building; the unit of measure of gain is Ns / m.
The predefined machines within the program, like real machines, are mainly subject to three mechanical constraints that define their potential: the maximum force generated by the actuator, the speed and the maximum stroke of the mobile mass:
- the force of the actuator to move the mobile mass is limited by the maximum pressure of 315 bar that can be reached by the hydraulic system of the machine; the maximum pressure is in turn limited by the servo-valve;
- considering the piston section of the machines, the maximum force that each of them is able to generate is equal to 220 kN;
- the speed at which it is possible to move the mobile mass is limited by the maximum flow rate of oil that can pass through the servo-valve; the maximum speed is 5 m / s;
- the stroke of the actuator is limited to ± 500 mm (+100 mm for braking).
To respect these technological limits, it is necessary to introduce saturations within the numerical model so that these constraints are satisfied:
- saturation in strength: | 𝐹𝑐𝑚б𝑥| = 220 𝑘𝑁;
- speed saturation: | 𝑣𝐴𝑀𝐷𝑚б𝑥| = 5 𝑚 / 𝑠;
- saturation in running: | 𝑠𝐴𝑀𝐷𝑚б𝑥| = 0.5 𝑚.
As regards the predefined systems, the limits are set automatically within AMDesign and are taken into account only for some types of simulation which will be explained later in this paragraph.
The saturations described above determine the performance of the system. Observe that the behavior of the machines is influenced by the dynamic properties of the structure.
In fact, if the structure oscillates at low frequencies, the moving mass of the AMD will also oscillate at low frequencies. When oscillating at low frequencies, with the same force, the displacement of the moving mass of the AMD is much greater than the oscillation of the same on a more rigid construction. The control force of each machine can be expressed in absolute value as:
𝐹𝑐= 𝑚𝐴𝑀𝐷∙ 𝑎𝐴𝑀𝐷
Force fixed 𝐹𝑐, and hence the acceleration 𝑎𝐴𝑀𝐷, the speed and displacement of the mobile mass of the AMD (in the simplified hypothesis that the machine responds only to the first natural frequency of the structure) depend on its oscillation frequency ω:
𝑣𝐴𝑀𝐷= 𝑎𝐴𝑀𝐷/ 𝜔
𝑠𝐴𝑀𝐷= 𝑎𝐴𝑀𝐷/ 𝜔2
With the same strength Fc (and therefore of acceleration 𝑎𝐴𝑀𝐷), if 𝜔 decreases, the displacement of the AMD 𝑠𝐴𝑀𝐷 increases proportionally to 1 / 𝜔2, while the speed of the AMD 𝑣𝐴𝑀𝐷 increases proportionally to 1 / 𝜔. For this reason, the system that acts on a particularly flexible structure, where the value of 𝜔 is low, could reach the saturations in speed and / or displacement, losing its effectiveness in reducing the oscillations of the construction, as the machine it would not be able to express all its potential in terms of control force discharged into the roof, acting with degraded performance.
This aspect must be taken into consideration in the numerical simulation phase for the design of the system and for the evaluation of the results obtained.
Within the AMDesign application, it is possible to carry out three different types of simulation, which differ according to the degree of detail with which you want to simulate the behavior of the active system:
- ideal system;
- constrained or constrained system;
- real system.
The system simulated as an ideal has no limit on the saturations seen above. Therefore, simulating the machines in this way, the software, in the course of the analyzes, will treat the machine as an ideal viscous heatsink that has no limit of any kind.
The constrained system, on the other hand, presents the saturations in force, speed and displacement, as it happens in reality. For this reason, the simulation will be much more complete than the ideal one.
The simulations with the real system consider, in addition to the three saturations, the dynamics of the system, through the definition of a specific transfer function. For the preset machines, the default transfer function was defined through suitable experimental tests.
The figure shows the AMDesign screen relating to the board Active control design.
"Active Control Design" panel
Through the analysis process, it will be essential to properly calibrate the parameter relating to the Control Gain which is a fundamental parameter in the design process of the AMD for the structure in question. The higher the value, the higher the force required from the installed AMDs. In the case of simulations different from the ideal ones, the Gain value will be influenced by the saturation limits seen above.
With the help of the SAP2000 ® instance to identify the node labels, it is necessary to select the nodes of the model where you want to download the control force of each single machine unit placed on the coverage plane. It is also necessary to identify a sensor application node near the roof and a node for the collinear sensor provided at the base of the building, in order to allow the program to calculate the relative speed in the analysis phase.
At this point, the active control system for the seismic protection of the structure is completed.
System architecture
In this panel, through an interactive mirror, it is possible to view the positioning of the AMDs designed in the previous tab.
It is possible to export a .png file depicting the positioning of the AMDs and sensors, showing a planimetric view of the roof plan belonging to the building.
Setting of the analysis in time history
In this tab it is possible to set a load case to carry out linear and / or non-linear dynamic time-history analyzes. The input approach is similar to the one present within the SAP2000 ® software.
The first input data is the sample time or the frequency at which the accelerogram data were sampled. To allow greater flexibility in the analysis phase and to meet the requirements of the Technical Regulations for Construction of 2018 at §7.3.5, AMDesign allows you to define two different acceleration histories for the two directions. The input files for the accelerograms, just like in the SAP environment, must be constructed by setting a single column in which only the accelerometric data are present.
It is then necessary to define the configuration for carrying out the analyzes, setting the simulation duration time and the time step for solving the solving equations.
If deemed necessary, it is also possible to define a Rayleigh structural damping.
In the case of non-linear analyzes, the program allows you to choose the type of solution (direct or modal integration), the possible initial load case (to take into account the static gravitational loads), the modal load case (only for FNA) and any geometric effects of the second order (only for the solution that provides for the direct integration of the equation of motion).
Once the data has been entered in this panel, it is possible to move on to the analysis phase.
Carrying out the analyzes
This sheet allows you to carry out the structural analyzes for the equipped construction of the previously designed active control system, starting from the data entered in the panel relating to the definition of the dynamic load case.
Before running the simulations it is useful to verify the correctness in the definition of the inputs within the previous panels. This operation is simple because it will be enough to check that all the circular light signals are green.
The analyzes within AMDesign are carried out through a complex simulator that allows the interaction between the SAP2000 ® software and Matlab ®. The first software is used to simulate the temporal history of the response of the structure subject to both the ground movement and the force released by the designed seismic protection system. The second software, on the other hand, simulates the control logic and the behavior of the machines in providing the force required by the control logic itself. The operating principle is illustrated in Figure 2: at each step, the time history is processed by the finite element software; the output is thus read by the Matlab ® code and, exactly as it would happen in reality, the control algorithm calculates the forces that must be released by the roofing machines in the next step, analyzing the motion of the structure at the points where the sensors. The calculated forces are thus exerted on the structure and the cycle repeats itself continuously. The forces delivered by the seismic protection system are considered to act, for each AMD, at the points chosen in the machine definition phase.
During the analysis process, the application allows you to view the salient information regarding the structure, in terms of displacement in coverage, and inherent to the AMD, in terms of control force. This information allows, in a rapid way, to evaluate the contribution of the system in terms of improvement on the structure and allows to check that the machines are working correctly.
The graphs are updated with a frequency value set by the user through the update plot command.
